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Population Growth and Exam Review!

+Populus Review Nt = N0ert

What does this equation model in Populus? Density-independent growth of a closed population:

continuous time formulation

Nt : is the population size at time t N0 : is the initial population size e : 2.718 (base of a natural log, a mathematical constant) r : instantaneous per capita rate of growth

+Populus Review Pt. 2 Nt = λt N0

What does this equation model in Populus?

Density-independent growth of a closed population: discrete time formulation.

Nt : is the population size at time t

N0 : is the initial population size

λ: is the per capita rate of growth per unit time t

Remember the Hint: λ= ert

(And remember that e is a mathematical constant…)

+Geometric Growth with Discrete Generations

+Continued…

+Terms to know: Distribution of a population: includes the size, shape, and

location of the area it occupies Abundance: the total number of individuals, or biomass, of

a species present in a specified area (p.200) Density: the number of individuals in a population per

unit area (p. 200) Top-down Control: the control or influence of consumers

on ecosystem processes Bottom-up Control: control of a community or ecosystem

by physical or chemical factors such as temperature or nutrient availability (p. 397)

Carrying capacity (K): the maximum population of a species that a particular ecosystem can sustain (p. 245)

+Continued… Cohort: a group of individuals of the same age (p.226) Cohort life table: a life table based on individuals born (or beginning

life in some other way) at the same time (p.226) Dependent variable: the variable traditionally plotted on the

vertical, or “Y” axis of a scatter plot Ecology: the study of the relationships between organisms and the

environment (p.1) Stable Age Distribution: a population in which the proportion of

individuals in each age class is constant, as a result of age specific survival, lx, and age specific reproduction, mx, remaining constant over time

Ecosystem: a biological community plus all of the abiotic factors influencing that community

Trophic Cascade: effects of predators on prey that alter abundance, biomass, or productivity of a population, community, or trophic level across more than one link in the food web.

+ Exponential Population Growth: population growth that produces a J-shaped pattern of population increase. In exponential population growth, the change in numbers with time is the product of the per-capita rate of increase, r, and population size, N. (p.243)

Geometric Population Growth: population growth in which generations do not overlap and in which successive generations differ in size by a constant ratio. (p. 242)

Geometric Rate of Increase: (λ) the ratio of the population size at two points in time: λ= Nt + 1lNt , where Nt + 1 is the size of the population at some earlier time. (p.233)

Life Table: a table of age-specific survival and death, or mortality, rates in a population. (p.226)

Sigmoidal population growth curve: an S-shaped pattern of population growth, with the population size leveling off at the carrying capacity of the environment

+Geometric and Exponential Population Growth In the presence of abundant resources, populations can

grown at geometric or exponential rates Phlox drumondii grow in discrete annual pulses. Populations

of insects that produce a single generation a year also grow in pulses.

 Growth by any population with pulsed reproduction can be modeled as geometric population growth, in which successive generations differ in size by a constant ratio.

We can compute the growth of a population or organisms whose generations do not overlap by simply multiplying λ times the size of the population and the number of offspring produced by this population during a year.

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What does N signify?

What does λ signify?

What is the equation used to determine λ?

+Exponential Growth

Continuous population growth in an unlimited environment can be modeled as exponential population growth:

The exponential growth equation expresses the rate of population growth, which is the change in numbers with change in time, as the per capita rate of increase, r, times the population size, N.

In the exponential model, r, is a constant, whereas N is a variable.Therefore, as population size, N, increases, the rate of population increase, dN/dt, gets larger and larger.

+Population Dynamics: Patterns of Survival A survivorship curve summarizes the pattern of

survival in a population. Life Tables: “bookkeeping devices”, list mortality, in a

population. Cohort Life Table vs. Static Life Table Age distribution: consists of the proportion of

individuals of different ages within a population. You can use an age distribution to estimate survival by

calculating the difference in proportion of individuals in succeeding age classes

+Three Types of Survivorship Curves:

Which of these illustrates the pattern of survival in mud turtles?

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+Is this population growing?

+ X = Age (days) nx = Number surviving to day x

lx = Proportion surviving to day x

mx = Average number of seeds per individual during time interval

lxmx = Multiplication of the proportion surviving to day x and the average number of seeds per individual during time interval

R0 = the net reproductive rate per individual

What does an R0 > 1.0 indicate about this population???

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What is the generation time?

What is R0?

Is this population growing?

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+Important! λ= geometric rate of increase n = sample size ΣX = sum of measurements of observations a = Y intercept b = regression coefficient, slope of the line R0 = net reproductive rate

T = generation time r = per capita rate of increase K = carrying capacity Imax = maximum per capita rate of increase; intrinsic rate of increase

N = population size

+ Nt : number of individuals at time t

N0 : initial number of individuals

e : base of natural logarithms μ: true population mean α: significance level X : independent variable Y : dependent variable t : time r selection: a term referring to the per capita rate of

increase; a form of natural selection favoring higher population growth rate. r selection is predicted to be strongest in disturbed habitats (p. 152)

+What is K?Carrying capacity

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+Body size and K

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